Description

Analysis to determine the most cost-effective and environmentally beneficial time of day to use energy, by comparing the relationship between electricity usage, weather, and electricity price in Ottawa, Toronto, and Niagara Falls.

Electricity supply and consumption change over time in three cities (Year) part I

Almost all the peak demand happen in winter and summer. Toronto uses significantly more electricity than other cities, and more volatile Overall, Toronto’s peak electricity demand has a certain downward trend over the years, Ottawa and Niagara are relatively stable. In contrast, Ottawa has the lowest electricity demand per capita, Niagara the highest, and Toronto is in the middle. Ottawa is the most efficient in terms of electricity demand

Electricity supply and consumption change over time in three cities (Year) part II

## `summarise()` has grouped output by 'month_year'. You can override using the
## `.groups` argument.

power output generation and demand are similar, with peaks occurring in summer and winter

Electricity supply and consumption change over time in three cities (Year) part III

If we look at demand and output together, we will find that they always show the same trend.

The only difference occurs in 2022. In this year, the demand in summer is higher than that in winter, but the output is the opposite.

Electricity supply and consumption change over time in three cities (Hour) partI

demand_hour <- demand_data %>% select(-month_year,-date) %>%
  pivot_longer(
    -hour,
    names_to = "city", 
    values_to = "volumn"
    )

demand_hour <- aggregate(demand_hour$volumn, by=list(demand_hour$hour,demand_hour$city),mean) %>% 
 rename(Hour=Group.1,city=Group.2,demand = x) %>%
  mutate(hours=as.character(Hour))

mean <- demand_hour%>% group_by(city)%>%summarise(mean_val=quantile(demand,0.6))

demand_hour %>% 
  ggplot(aes( x = reorder(hours,Hour),y = demand, colour = city,group=city))+
  geom_line(aes(color=city)) +
  geom_point(size=2) +
  geom_hline(data=mean,aes(yintercept=mean_val,color=city,linetype="60 percentiles of the demand(base load)"))+ #cite 1
  theme_minimal() +
    labs(
    x = 'Period (hour)',
    y = 'Power demand(MW)',
    colour = 'city'
  )

lowest demand happen on 4am and start increase untill reach the peak which is 6pm. After 6pm, the demand decrease. When we look at demand from the perspective of hours, based on the base load(60%), from 10 am to 9 pm, the demand exceeds the base load. So if you want to be more environmental friendly, use the electricity before 10am or after 9pm.

Electricity supply and consumption change over time in three cities (Hour) partII

## `summarise()` has grouped output by 'delivery_date', 'month_year'. You can
## override using the `.groups` argument.
## Adding missing grouping variables: `delivery_date`, `month_year`

Power output is pretty much the same as demand. lowest output happen on 3am and highest happen on 6pm.

Electricity supply and consumption change over time in three cities (Hour) partIII

## `summarise()` has grouped output by 'hours'. You can override using the
## `.groups` argument.

If we look at demand and output together, they are almost showing the same trend.

Electricity supply and consumption change over time in three cities (Hour) partIV

df2 %>% select(Time,Hour,demand,capacity) %>%
ggplot(aes(x=demand,y=capacity,size=demand/capacity,color=Hour),alpha=0.8) +
  geom_point() +
  stat_smooth(method = glm,level=0.95) +
  scale_size_continuous(range = c(2, 10)) +
  geom_label_repel(aes(label = Hour),size=3)

method = glm,level=0.95 we need to prevent using electricity on the hour above the line, which is 6pm to 9pm since for the same demand it need higher capacity which may increase power plant emissions. Switch them to the hour below the line may be a good idea.

Changes in Electricity Rates Over Time (year)

getPrice <- function(filename){
  temp <- read_csv(filename,skip = 3, col_names = TRUE,show_col_types = FALSE) %>%
  clean_names() %>%
  select(date,hour,hoep)
  return(temp)
}

price_data <- tibble()
for (i in 2019:2023)
{
filename = paste("PUB_PriceHOEPPredispOR_",i,".csv",sep = "")
price_data <- price_data %>% bind_rows(getPrice(filename)) %>%
  mutate(month_year = format(as.Date(date), "%Y-%m"))
}

price_month <- price_data %>%
  select(month_year,hoep) %>%
  group_by(month_year) %>%
  summarise(price = mean(hoep))

price_month %>% 
  ggplot(aes( x = month_year, y = price))+
  geom_line(aes(size=2),group=1,color="darkgreen") +
  theme_minimal() +
    labs(
    x = 'Period (year)',
    y = 'price($ CAD per MWh)'
  ) +
  theme(axis.text.x = element_text(angle=90,hjust=0.5, vjust=0.5))

There is a very, very significant increase in electricity prices from summer 2022. The possible reason is that the war in Ukraine has caused global energy problems

Changes in Electricity Rates Over Time (hour) partI

price_hour <- price_data %>%
  select(hour,hoep) %>%
  group_by(hour) %>%
  summarise(price_val=mean(hoep)) %>%
  mutate(hours=as.character(hour))

price_hour %>% 
  ggplot(aes( x = reorder(hours,hour), y = price_val))+
  geom_line(aes(size=2),group=1,color="darkgreen") +
  theme_minimal() +
    labs(
    x = 'Period (hour)',
    y = 'price($ CAD per MWh)'
  ) +
  theme(axis.text.x = element_text(angle=90,hjust=0.5, vjust=0.5))

If we look at the price from an hourly perspective，Two peaks occur at 10 am and 6:00 pm The difference from the demand is that the price shows a decline from 10am in the morning to 2pm in the afternoon. If you want to be more economical, you can try to use electricity between 10pm and 7am,Especially between 1am and 5am，During this time period, the electricity bill is basically equal to 0.

Changes in Electricity Rates Over Time (hour) partII

df3 <- demand_hour2 %>%
  left_join(price_hour,by=c("hours"="hours")) %>%
  select(-hour)

df3 %>%
  ggplot(aes(x=mean_val,y=price_val,size=price_val,color=Hour),alpha=0.8) +
  geom_point() +
  stat_smooth(method = glm,level=0.99) +
  scale_size_continuous(range = c(2, 10))+
  labs(
    x = 'Demand (MW)',
    y = 'price($ CAD per MWh)'
  ) +
  geom_label_repel(aes(label = hours, fontface = "bold"),size=3)

method:glm, level:0.99

1am to 6am is the most economical It is relatively economical to use electricity between 1pm and 4pm. And 8am to 10am is relatively the least economical

Temperature changes over time in three cities (year)

temp_hour <- tibble()
cities <- c("6139449","6105978","6158355")
  
months <- c("01","02","03","04","05","06","07","08","09","10","11","12")
for(i in cities)
{
for (j in 2019:2023)
{
  for(k in months)
{
filename = paste("en_climate_hourly_ON_",i,"_",k,"-",j,"_P1H.csv",sep = "")
if (file.exists(filename))
{
  temp <-read_csv(filename,col_names = TRUE,show_col_types = FALSE) %>%
  clean_names()%>%select(station_name,temp_c,date_time_lst,day,time_lst) %>%
  mutate(hour=as.numeric(gsub(".?([0-9]+).", "\\1",date_time_lst)))%>%select(-time_lst)%>%mutate(month_year = format(as.Date(date_time_lst), "%Y-%m"))
  
  temp_hour <- temp_hour %>% bind_rows(temp)
}
}
}
}

temp_hour <-temp_hour%>%pivot_wider(names_from = station_name, values_from = temp_c)%>%clean_names()%>%setnames(old = c('welland_pelham','ottawa_cda_rcs','toronto_city'),new = c('Niagara','Ottawa','Toronto'))

temp_month <- temp_hour %>% 
  select (month_year,Niagara,Ottawa,Toronto) %>% 
  pivot_longer(-month_year,
              names_to = "city",
              values_to = "temp") %>%
  drop_na() %>%
  group_by(month_year,city) %>%
  summarise(mean_temp=mean(temp)) 

temp_month %>% 
  ggplot(aes( x = month_year, y = mean_temp,group=city,color=city))+
  geom_line(aes(color=city)) +
  geom_point()+
  geom_smooth(method='loess',aes(group=city))+
  theme_minimal() +
    labs(
    x = 'Period (year)',
    y = 'Average Temperature(˚C)'
  ) +
  theme(axis.text.x = element_text(angle=90,hjust=0.5, vjust=0.5))

Toronto is the warmest and Ottawa is the coldest.

Temperature is similar in summer for those three cities. But for winter, Ottawa is much more colder, maybe it’s due to great lake effect.

global warming is not trun for Ontario.

Temperature changes over time in three cities (hour)

temp_data <- tibble()
temp_hour<- tibble()
cities <- c("6139449","6105978","6158355")
months <- c("01","02","03","04","05","06","07","08","09","10","11","12")
for(i in cities)
{
for (j in 2019:2023)
{
  for(k in months)
{
filename = paste("en_climate_hourly_ON_",i,"_",k,"-",j,"_P1H.csv",sep = "")
if (file.exists(filename))
{
  temp <-read_csv(filename,col_names = TRUE,show_col_types = FALSE) %>%
  clean_names()%>%select(station_name,temp_c,date_time_lst,day,time_lst) %>%
  mutate(hour=as.numeric(gsub(".*?([0-9]+).*", "\\1",time_lst)))%>%select(-time_lst)%>%mutate(month_year = format(as.Date(date_time_lst), "%Y-%m"))
  
  temp_data <- temp_data %>% bind_rows(temp)

}
}
}
}

temp_data<-temp_data%>%pivot_wider(names_from = station_name, values_from = temp_c)%>%clean_names()%>%setnames(old = c('welland_pelham','ottawa_cda_rcs','toronto_city'),new = c('niagara','ottawa','toronto'))


temp_hour <- temp_data %>%select (hour,niagara,ottawa,toronto) %>% pivot_longer(-hour,names_to = "city",values_to = "temp") %>%drop_na() %>% group_by(hour,city) %>%summarise(mean_temp_hour=mean(temp))#%>%pivot_wider(names_from = city, values_from = mean_temp)


ggplot(temp_hour, mapping = aes(x = hour, y = mean_temp_hour, color = city) ) + geom_line()+ 
  geom_point()+
  labs(
    x = 'Period (Hours)',
    y = 'Temperature(˚C)')

Toronto and Niagara are similar, Ottawa still the coldest. lowest temperature always happen on 5am and highest is around 2-3pm.

Electricity supply and consumption change over temperature in three cities

temp_hour2 <- temp_data  %>%pivot_longer(cols = c('niagara', 'ottawa', 'toronto'), names_to = 'city', values_to = 'temp') %>% select(month_year, city, temp)%>% drop_na()%>% group_by(city, month_year) %>% summarise(mean_temp = mean(temp))

demand_temp <- left_join(demand_month,temp_hour2,by = c("city"="city","Time"="month_year"))

demand_temp %>%
ggplot(aes( x = mean_temp,y = demand, colour = city,group=city))+
geom_line(aes(color=city)) +
geom_point(size=2) +
geom_smooth(method = "glm")+
theme_minimal() +
labs(
x = 'Temp (C)',
 y = 'Power demand(MW)',
 colour = 'city' )

Looks like Toronto has a positive correlation between temperature and demand.

Ottawa has a negative correlation between temperature and demand.

Niagara is neutral.

Conclusion

If you want to be more environmental friendly, use electricity before 10am or after 9pm.

If you have to, 12pm-2pm is the best choice.

If you want to save money, try to go between 1am and 6am

If you have to, 1pm-4pm is the best choice

Future work

Global Adjustment

regression on price,demand,weather

some extreme weather conditions

benford analysis

Appendices

References

SessionInfo

sessionInfo()

## R version 4.2.2 (2022-10-31)
## Platform: aarch64-apple-darwin20 (64-bit)
## Running under: macOS Ventura 13.3
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggtrendline_1.0.3      data.table_1.14.8      benford.analysis_0.1.5
##  [4] tictoc_1.1             patchwork_1.1.2        scales_1.2.1          
##  [7] ggrepel_0.9.2          janitor_2.1.0          readxl_1.4.1          
## [10] lubridate_1.9.0        timechange_0.2.0       knitr_1.41            
## [13] forcats_1.0.0          stringr_1.5.0          dplyr_1.0.10          
## [16] purrr_1.0.1            readr_2.1.3            tidyr_1.2.1           
## [19] tibble_3.1.8           ggplot2_3.4.0          tidyverse_1.3.2       
## [22] flexdashboard_0.6.1   
## 
## loaded via a namespace (and not attached):
##  [1] httr_1.4.4          sass_0.4.4          splines_4.2.2      
##  [4] bit64_4.0.5         vroom_1.6.0         jsonlite_1.8.4     
##  [7] modelr_0.1.10       bslib_0.4.2         assertthat_0.2.1   
## [10] highr_0.10          googlesheets4_1.0.1 cellranger_1.1.0   
## [13] yaml_2.3.6          lattice_0.20-45     pillar_1.8.1       
## [16] backports_1.4.1     glue_1.6.2          digest_0.6.31      
## [19] rvest_1.0.3         snakecase_0.11.0    colorspace_2.0-3   
## [22] Matrix_1.5-1        htmltools_0.5.4     pkgconfig_2.0.3    
## [25] broom_1.0.2         haven_2.5.1         tzdb_0.3.0         
## [28] googledrive_2.0.0   mgcv_1.8-41         farver_2.1.1       
## [31] generics_0.1.3      ellipsis_0.3.2      cachem_1.0.6       
## [34] withr_2.5.0         cli_3.6.0           magrittr_2.0.3     
## [37] crayon_1.5.2        evaluate_0.19       fs_1.5.2           
## [40] fansi_1.0.3         nlme_3.1-160        xml2_1.3.3         
## [43] tools_4.2.2         hms_1.1.2           gargle_1.3.0       
## [46] lifecycle_1.0.3     munsell_0.5.0       reprex_2.0.2       
## [49] compiler_4.2.2      jquerylib_0.1.4     rlang_1.0.6        
## [52] grid_4.2.2          rstudioapi_0.14     labeling_0.4.2     
## [55] rmarkdown_2.19      gtable_0.3.1        DBI_1.1.3          
## [58] R6_2.5.1            fastmap_1.1.0       bit_4.0.5          
## [61] utf8_1.2.2          stringi_1.7.12      parallel_4.2.2     
## [64] Rcpp_1.0.9          vctrs_0.5.1         dbplyr_2.3.0       
## [67] tidyselect_1.2.0    xfun_0.36

Final Project Report

final report

Yangyijun Gao(300262073) & Pratik Jariwala & Prayag Asokan Nandini

2023-04-08